“I heard my name in the broadcast, asking me to get off the plane,” Watson said. “I didn’t know what was going on. I thought we left something or we were on the wrong flight.”

Watson was then approached by a flight attendant, who refused to tell him the reason for the broadcast, but said: “You need to exit the aircraft immediately.”

“So I walked by the people who we just walked by to get to our seats,” Watson said.

Watson then ran into the same gate agent he had tweeted about.

“She [the agent] said I was a safety threat,” Watson said. “I was shocked. There was no use of profanity, there were no threats made. How was I a safety threat?”

Watson said the agent threatened to call the cops if he didn’t delete the tweet that included her first name and initial of last name.

“I was taken aback by the situation. My two kids were crying,” Watson said. “She watched me as I deleted the tweet.”

The gate agent then allegedly summoned Watson and his two children to get back on the same flight.

“So we walked through the same passengers the third time,” Watson said.

“The point is not the order of boarding,” Watson said. “The point is how she responded.”

Southwest Airlines could not be immediately reached for comment by ABC News. But the airline issued a statement to a local CBS affiliate confirming that a customer was removed for a short time and continued on to Minneapolis. The incident is under review, Southwest noted.

The follow-up from the incident on Sun. with @SouthwestAir is now a double insult. Choose a kinder airline. #neveragain Family deplaned?